HALL
发表于 2025-3-25 06:59:12
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和平主义者
发表于 2025-3-25 09:17:46
Plane Curve Singularities,rsection multiplicity of two (irreducible) plane curve singularities (., o) and (., o). This number can be calculated as follows. Consider the normalization ℂ{.} of .., and let (., o) be given by . = 0. Via the inclusion .. ∈ℂ{.}, we can consider at . as an element of ℂ{.}. Then the intersection mul
命令变成大炮
发表于 2025-3-25 11:57:55
Classification of Simple Hypersurface Singularities,acy Theorems. Let m be the maximal ideal of ℂ{..,... ,..}. A function / is called (right) .-determined if for all elements . with . ∈ m.. the functions / and . are right equivalent. In particular, a .-determined . is right equivalent to a polynomial of degree at most .. A function is called finitely
把手
发表于 2025-3-25 16:57:31
Textbook 2000ll do in this book, as the "commutative algebra" one needs in local analytic geometry is somewhat more difficult: one has to cope with convergence questions. The most prominent and important example is the substitution of division with remainder. Its substitution in local analytic geometry is called
铺子
发表于 2025-3-25 23:08:41
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Ostrich
发表于 2025-3-26 00:54:53
0932-7134 (over an algebraically closed field). As one often reads in prefaces of int- ductory books on algebraic geometry, it is not so easy to develop the basics of algebraic geometry without a proper knowledge of commutative algebra. On the other hand, the commutative algebra one needs is quite difficult t
过分
发表于 2025-3-26 07:11:41
Approximation Theorems, system of analytic equations has a formal solution (which is sometimes really not convergent) then we can find a convergent solution to this system. Even more, we can approximate the formal one by convergent ones up to a given order.
肉身
发表于 2025-3-26 09:30:02
Standard Bases,s regular of order . in ... For any . ∈ ℂ . we have a unique representation . with . a polynomial of degree less than .. From the uniqueness statement in the Weierstraß Division Theorem, it follows without difficulty that the remainder . only depends on the coset .) of (.). Of course, the remainder . depends on the choice of ...
collagen
发表于 2025-3-26 15:32:35
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Explicate
发表于 2025-3-26 17:42:02
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